A calculus question about using shells to find volume?

Find the volume of the solid generated by y=x^0.5, x=4, y=0 revolved around the y-axis

A calculus question about using shells to find volume?
The formula for shells is 2pi * Integral from a to b of (distance from axis of revolution) * (distance from base to Fx) dx



The reason this works is like because your finding the surface area of an infinite number of cylinders to get the volume. That's how I think about it at least. its like that because 2pi * distance from axis of revolution is like the radius, and distance from teh base to Fx is like the height.



So,

2pi * integral from 0 to 4 of x * x^0.5 dx

2pi * integral from 0 to 4 of x^1.5 dx



From here just do a nice simple integration.





Edit: Drawing a diagram helps too.